AMC 10 Algebra — Paper 1
Free AMC 10 Algebra practice paper: 30 questions on quadratics, Vieta, sequences, logarithms and functional equations, with worked solutions.
About this test
AMC 10 Algebra — Paper 1 is a full 30-question paper you attempt online in 75 minutes. It follows the American Mathematics Competition 10 pattern, so the timing, the question style and the marking match the real exam. There is no negative marking, so it is worth attempting every question. Leaving a question blank still earns 1.5 marks.
You get your score the moment you submit, question by question, with a step-by-step solution to every problem. 25 questions in 75 minutes. A high score qualifies for the AIME.
What it covers
Sections
- Vieta — 3 questions
- Exponents — 2 questions
- Sequences — 4 questions
- Absolute value — 2 questions
- Systems — 4 questions
- Quadratics — 4 questions
- Logarithms — 2 questions
- Functional equations — 2 questions
- Inequalities — 2 questions
- Word problems — 2 questions
- Radicals — 1 question
- Polynomials — 2 questions
Difficulty spread
- 5 easy questions
- 17 medium questions
- 8 hard questions
Before you start
15 questions · 45 minutes.
- Each correct answer scores 6 points.
- Each unanswered question scores 1.5 points.
- A wrong answer scores 0 — a blank is worth more than a guess unless you can eliminate at least three options.
- No calculators. Rough work on paper.
This paper covers Algebra only, so a weak score points at one topic rather than leaving you guessing.
A look at the questions
Questions people ask
How hard is this AMC 10 algebra paper?
It is pitched at the real contest. The opening questions are approachable, the middle band is where most AMC 10 scores are decided, and the last eight sit at the difficulty that separates AIME qualifiers.
What topics does it cover?
Quadratics and Vieta's formulas, systems of equations, sequences and series, functional equations, inequalities, logarithms and exponents, absolute value, and word problems that hide an algebraic structure.
How is it scored?
Exactly like the real AMC 10: 6 points for a correct answer, 1.5 for a blank, 0 for a wrong one. A wild guess costs you the 1.5, so leave a question blank unless you can eliminate at least three options.
How long should it take?
75 minutes for 30 questions — deliberately tighter than three minutes each, because working accurately under time pressure is part of what the AMC actually tests.